At times I have used Maxima, Matlab, and Mathematica to solve differential equations but to give specific recommendations more input about the use case is needed.
As powerful as possible? In particularly, I’m trying to solve an infinite-horizon optimal control problem with restrictions on what the inputs can be (e.g., not lower than zero), and the resulting equations are quite gnarly. The premium version of Wolfram Alpha couldn’t really deal with them.
What level and type of application do you need?
Wolfram Alpha can do differential equations for example: https://www.wolframalpha.com/input/?i=y%27+%3D+y+%2B+sin+x
At times I have used Maxima, Matlab, and Mathematica to solve differential equations but to give specific recommendations more input about the use case is needed.
As powerful as possible? In particularly, I’m trying to solve an infinite-horizon optimal control problem with restrictions on what the inputs can be (e.g., not lower than zero), and the resulting equations are quite gnarly. The premium version of Wolfram Alpha couldn’t really deal with them.
In that case, you are probably beyond what I can help you with.